This poem is meant to show how bad life is in London. The lines that you mention help to paint this picture.
Harlots are prostitutes -- that is important to understanding these lines.
Blake is saying that, as he walks through London, he hears and sees many bad things. The last of these are described in the words you mention.
There, he is describing the cursing of a young prostitute, presumably as she gives birth to a baby. Her baby's innocence is lost because of her cursing. This shows how even at the beginning of life, things are already bad for the poor of London.
The enotes Study Guide to Blake's "London" says the following concerning the lines you ask about:
The final stanza of the poem is set in darkness—Blake is listening in the midnight streets to the cries of young prostitutes as they curse the men who victimize them, the wives who are equally victims, and the religion that forces people to think that they must marry and stay married no matter what. “London” ends on a pessimistic note in which Blake reviles the one sacrament that should offer hope to present and future generations: marriage. Instead of being predicated on love and mutual respect, Blake sees it as something that enslaves the body and soul in much the same way that stanzas 2 and 3 point out that English laws victimize the less fortunate.
This final stanza reveals what sex, marriage and birth lead to in London. Blake offers in this work, as he does in numerous poems, a perspective that is opposite the usual. His collections, Songs of Innocence and Songs of Experience demonstrate how multiple perspectives exist for similar situations and circumstances. "London," which belongs to Experience, demonstrates a perspective that understands the dark side of London, a city that is not only the capitol of England, but the capitol of the British Empire.
How the youthful Harlots curse
Blasts the new-born Infants tear
And blights with plagues the Marriage hearse
The meaning of these three lines seems to be this. If men consort with prostitutes (harlots) they are very likely to pick up sexually transmitted diseases. The most common and most terrible of these diseases was syphilis, which was incurable. Then when some of these infected men got married, they would almost surely transmit the disease to their brides, who often were innocent young virgins. And, of course, when the wives became pregnant they would transmit the disease to their infants. Blake imagines the infants being so riddled with the disease that even their tears would be contaminated. Eventually a whole population could become infected, as is the case in modern times with AIDS in some parts of Africa.
According to the eNotes Study Guide on Blake's "London":
By choosing syphilis as the symbol for all that is wrong with England, Blake is able to condemn institutions and emotions that are sacred to most people: love and marriage.
Henrik Ibsen's play Ghosts (1882) is about how a young man's life is ruined by the fact that his father passed on the disease of syphilis to him at conception some twenty-six years earlier.